Cremona's table of elliptic curves

7812 = 2² · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 31+	Signs for the Atkin-Lehner involutions
Class	7812b	Isogeny class
Conductor	7812	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	1499904 = 28 · 33 · 7 · 31	Discriminant
Eigenvalues	2- 3+ -2 7+ -6 -2 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3471,78710]	[a1,a2,a3,a4,a6]
Generators	[7:234:1] [22:114:1]	Generators of the group modulo torsion
j	669088897776/217	j-invariant
L	4.8956382564234	L(r)(E,1)/r!
Ω	2.1629340343919	Real period
R	1.5089497810475	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	31248be2 124992e2 7812a2 54684e2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7812b2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	+	-2	+	-6	-2	-8	-4	-2	-6	+	-10	-10	12	-2	6	6	-2	4	8	6	0	-12	0	-2

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Quadratic twists for elliptic curve 7812b2

-4	8	-3	-7
31248be2	124992e2	7812a2	54684e2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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